Poker Probability with hands of 6 cards

Question

I am trying to answer Question 1(d). A valid hand would be Ace hearts, 10 hearts, 2 clubs, 7 clubs, Ace spades, J spades.

My attempts have given me 2 different answers that I am unsure of.

What I did was I had to choose 3 suits from 4, then choose 2 cards from each of those suits. When choosing the 2 cards from each suit, do I have to do it 3 times? Would it be 4C3 x (13C2)^3 or 4C3 x 13C2

Thank you.

Answer 1

You are counting ways to select: two from thirteen kinds for each of three from four suits.$$({^{13}\mathrm C_2})^3\cdot{^4\mathrm C_3}$$

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Note: ${^{13}\mathrm C_2}\cdot{^4\mathrm C_3}$ would count ways to select the same two from thirteen kinds in three from four suits.